A Perturbation of an Abstract Volterra Equation
Copyright policy )A Perturbation of an Abstract Volterra Equation
This paper discusses the existence of solutions to equations of the form $u(t,x) + \smallint _0^t a(t - s)[Au(s,x) + g(u(s,x))]ds = f(t,x)$ where A is a differential operator on $L^2 (\Omega ),\Omega $ a bounded open subset of $R^n $, and g is a discontinuous real-valued function which is not necessarily monotone increasing.
Volterra integral equations, perturbation, abstract Volterra equation, existence of solutions, Abstract integral equations, integral equations in abstract spaces, Theoretical approximation of solutions to integral equations, compactness, monotonicity
Volterra integral equations, perturbation, abstract Volterra equation, existence of solutions, Abstract integral equations, integral equations in abstract spaces, Theoretical approximation of solutions to integral equations, compactness, monotonicity
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